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geometry.rs
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use feos_core::{EosResult, EosUnit};
use ndarray::Array1;
use quantity::{QuantityArray1, QuantityArray2, QuantityScalar};
use std::f64::consts::{FRAC_PI_3, PI};
/// Grids with up to three dimensions.
#[derive(Clone)]
pub enum Grid {
Cartesian1(Axis),
Cartesian2(Axis, Axis),
Periodical2(Axis, Axis),
Cartesian3(Axis, Axis, Axis),
Periodical3(Axis, Axis, Axis),
Spherical(Axis),
Polar(Axis),
Cylindrical { r: Axis, z: Axis },
}
impl Grid {
pub fn new_1d(axis: Axis) -> Self {
match axis.geometry {
Geometry::Cartesian => Self::Cartesian1(axis),
Geometry::Cylindrical => Self::Polar(axis),
Geometry::Spherical => Self::Spherical(axis),
}
}
pub fn axes(&self) -> Vec<&Axis> {
match self {
Self::Cartesian1(x) => vec![x],
Self::Cartesian2(x, y) | Self::Periodical2(x, y) => vec![x, y],
Self::Cartesian3(x, y, z) | Self::Periodical3(x, y, z) => vec![x, y, z],
Self::Spherical(r) | Self::Polar(r) => vec![r],
Self::Cylindrical { r, z } => vec![r, z],
}
}
pub fn axes_mut(&mut self) -> Vec<&mut Axis> {
match self {
Self::Cartesian1(x) => vec![x],
Self::Cartesian2(x, y) | Self::Periodical2(x, y) => vec![x, y],
Self::Cartesian3(x, y, z) | Self::Periodical3(x, y, z) => vec![x, y, z],
Self::Spherical(r) | Self::Polar(r) => vec![r],
Self::Cylindrical { r, z } => vec![r, z],
}
}
pub fn grids(&self) -> Vec<&Array1<f64>> {
self.axes().iter().map(|ax| &ax.grid).collect()
}
pub(crate) fn integration_weights(&self) -> Vec<&Array1<f64>> {
self.axes()
.iter()
.map(|ax| &ax.integration_weights)
.collect()
}
pub(crate) fn integration_weights_unit<U: EosUnit>(&self) -> Vec<QuantityArray1<U>> {
self.axes()
.iter()
.map(|ax| &ax.integration_weights * U::reference_length().powi(ax.geometry.dimension()))
.collect()
}
}
/// Geometries of individual axes.
#[derive(Copy, Clone)]
#[cfg_attr(feature = "python", pyo3::pyclass)]
pub enum Geometry {
Cartesian,
Cylindrical,
Spherical,
}
impl Geometry {
/// Return the number of spatial dimensions for this geometry.
pub fn dimension(&self) -> i32 {
match self {
Self::Cartesian => 1,
Self::Cylindrical => 2,
Self::Spherical => 3,
}
}
}
/// An individual discretized axis.
#[derive(Clone)]
pub struct Axis {
pub geometry: Geometry,
pub grid: Array1<f64>,
pub edges: Array1<f64>,
integration_weights: Array1<f64>,
potential_offset: f64,
}
impl Axis {
/// Create a new (equidistant) cartesian axis.
///
/// The potential_offset is required to make sure that particles
/// can not interact through walls.
pub fn new_cartesian<U: EosUnit>(
points: usize,
length: QuantityScalar<U>,
potential_offset: Option<f64>,
) -> EosResult<Self> {
let potential_offset = potential_offset.unwrap_or(0.0);
let l = length.to_reduced(U::reference_length())? + potential_offset;
let cell_size = l / points as f64;
let grid = Array1::linspace(0.5 * cell_size, l - 0.5 * cell_size, points);
let edges = Array1::linspace(0.0, l, points + 1);
let integration_weights = Array1::from_elem(points, cell_size);
Ok(Self {
geometry: Geometry::Cartesian,
grid,
edges,
integration_weights,
potential_offset,
})
}
/// Create a new (equidistant) spherical axis.
pub fn new_spherical<U: EosUnit>(points: usize, length: QuantityScalar<U>) -> EosResult<Self> {
let l = length.to_reduced(U::reference_length())?;
let cell_size = l / points as f64;
let grid = Array1::linspace(0.5 * cell_size, l - 0.5 * cell_size, points);
let edges = Array1::linspace(0.0, l, points + 1);
let integration_weights = Array1::from_shape_fn(points, |k| {
4.0 * FRAC_PI_3 * cell_size.powi(3) * (3 * k * k + 3 * k + 1) as f64
});
Ok(Self {
geometry: Geometry::Spherical,
grid,
edges,
integration_weights,
potential_offset: 0.0,
})
}
/// Create a new logarithmically scaled cylindrical axis.
pub fn new_polar<U: EosUnit>(points: usize, length: QuantityScalar<U>) -> EosResult<Self> {
let l = length.to_reduced(U::reference_length())?;
let mut alpha = 0.002_f64;
for _ in 0..20 {
alpha = -(1.0 - (-alpha).exp()).ln() / (points - 1) as f64;
}
let x0 = 0.5 * ((-alpha * points as f64).exp() + (-alpha * (points - 1) as f64).exp());
let grid = (0..points)
.into_iter()
.map(|i| l * x0 * (alpha * i as f64).exp())
.collect();
let edges = (0..=points)
.into_iter()
.map(|i| {
if i == 0 {
0.0
} else {
l * (-alpha * (points - i) as f64).exp()
}
})
.collect();
let k0 = (2.0 * alpha).exp() * (2.0 * alpha.exp() + (2.0 * alpha).exp() - 1.0)
/ ((1.0 + alpha.exp()).powi(2) * ((2.0 * alpha).exp() - 1.0));
let integration_weights = (0..points)
.into_iter()
.map(|i| {
(match i {
0 => k0 * (2.0 * alpha).exp(),
1 => ((2.0 * alpha).exp() - k0) * (2.0 * alpha).exp(),
_ => (2.0 * alpha * i as f64).exp() * ((2.0 * alpha).exp() - 1.0),
}) * ((-2.0 * alpha * points as f64).exp() * PI * l * l)
})
.collect();
Ok(Self {
geometry: Geometry::Cylindrical,
grid,
edges,
integration_weights,
potential_offset: 0.0,
})
}
/// Returns the total length of the axis.
///
/// This includes the `potential_offset` and used e.g.
/// to determine the correct frequency vector in FFT.
pub fn length(&self) -> f64 {
self.edges[self.grid.len()] - self.edges[0]
}
/// Returns the volume of the axis.
///
/// Depending on the geometry, the result is in m, m² or m³.
/// The `potential_offset` is not included in the volume, as
/// it is mainly used to calculate excess properties.
pub fn volume<U: EosUnit>(&self) -> QuantityScalar<U> {
let length = (self.edges[self.grid.len()] - self.potential_offset - self.edges[0])
* U::reference_length();
(match self.geometry {
Geometry::Cartesian => 1.0,
Geometry::Cylindrical => 4.0 * PI,
Geometry::Spherical => 4.0 * FRAC_PI_3,
}) * length.powi(self.geometry.dimension())
}
/// Interpolate a function on the given axis.
pub fn interpolate<U: EosUnit>(
&self,
x: f64,
y: &QuantityArray2<U>,
i: usize,
) -> QuantityScalar<U> {
let n = self.grid.len();
y.get((
i,
if x >= self.edges[n] {
n - 1
} else {
match self.geometry {
Geometry::Cartesian | Geometry::Spherical => (x / self.edges[1]) as usize,
Geometry::Cylindrical => {
if x < self.edges[1] {
0
} else {
(n as f64
- (n - 1) as f64 * (x / self.edges[n]).ln()
/ (self.edges[1] / self.edges[n]).ln())
as usize
}
}
}
},
))
}
}